Question

A tire at 21°C has a pressure of 0.82 atm. Its temperature decreases to –3.5°C. If there is no volume change in the tire, what is the pressure after the temperature change?

Answer 1

The correct answer is A 0.75 atm

Answer 2

Answer : The pressure after the temperature change is, 0.75 atm.

Solution :

According to the Gay-Lussac's Law, the pressure is directly proportional to the temperature of the gas at constant volume and number of moles.

$P\propto T$     (At constant volume and number of moles)

Or,

$\frac{P_1}{P_2}=\frac{T_1}{T_2}$

where,

$P_1$ = initial pressure = 0.82 atm

$P_2$ = final pressure = ?

$T_1$ = initial temperature = $21^oC=273+21=294K$

$T_2$ = final temperature = $-3.5^oC=273+(-3.5)=269.5K$

Now put all the given values in the above formula, we get the final pressure of the gas.

$\frac{0.82atm}{P_2}=\frac{294K}{269.5K}$

$P_2=0.75atm$

Therefore, the pressure after the temperature change is, 0.75 atm